# Numerical Modeling of Coupled Fluid Flow and Geomechanical Stresses in a Petroleum Reservoir

01 Jun 2020-Journal of Energy Resources Technology-transactions of The Asme (American Society of Mechanical Engineers Digital Collection)-Vol. 142, Iss: 6

Abstract:
A fully coupled hydro and geomechanical model has been used to predict the transient pressure disturbance, reservoir deformation, and effective stress distribution in both homogeneous and heterogeneous reservoirs. The heterogeneous reservoir is conceptualized by explicitly considering the spatial distributions of porosity and permeability as against assuming it as constant values. The finite element method was used in the coupled model in conjunction with the poroelasticity. Transient pressure disturbance is significantly influenced by the overburden during the production in both homogeneous and heterogeneous reservoirs for all the perforation schemes. Perforation scheme 2 provides the optimum reservoir performance when compared with other three schemes in terms of transient pressure distribution and reservoir subsidence. It also has the ability to overcome both the water and gas coning problems when the reservoir fluid flow is driven by both gas cap and water drive mechanisms. A Biot–Willis coefficient is found to significantly influence both the pressure and stress distribution right from the wellbore to the reservoir boundary. Maximum effective stresses have been generated in the vicinity of the wellbore in the reservoir at a high Biot–Willis coefficient of 0.9. Thus, the present work clearly projects that a Biot–Willis coefficient of 0 cannot be treated to be a homogeneous reservoir by default, while the coupled effect of hydro and geomechanical stresses plays a very critical role. Therefore, the implementation of the coupled hydro and geomechanical numerical models can improve the prediction of transient reservoir behavior efficiently for the simple and complex geological systems effectively.

Topics: Fluid dynamics (57%), Permeability (earth sciences) (53%), Petroleum reservoir (51%)

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Abstract:
This work presents the prediction of thermal drawdown of an enhanced geothermal system (EGS) using artificial neural network (ANN). A three-dimensional numerical model of EGS was developed to generate the training and testing data sets for ANN. We have performed a quantitative study of geothermal energy production for various injection operating conditions and reservoir fracture aperture. Input parameters for ANN include temperature, mass flux, pressure, and fracture transmissivity, while the production well temperature is the output parameter. The Levenberg–Marquardt back-propagation learning algorithm, the tan-sigmoid, and the linear transfer function were used for the ANN optimization. The best results were obtained with an ANN architecture composed of eight hidden layers and 20 neurons in the hidden layer, which made it possible to predict the production temperature with a satisfactory range (R2 > 0.99). An appropriate accuracy of the ANN model was obtained with a percentage error less than (± 4.5). The results from the numerical simulations suggest that fracture transmissivity has less effect on thermal drawdown than the injection mass flux and temperature. From our results, we confirm that ANN modeling may predict the thermal drawdown of an EGS system with high accuracy.

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TL;DR: Hydrogen in an equiatomic CoCrFeMnNi high-entropy alloy leads not to catastrophic weakening, but instead increases both, its strength and ductility, which opens new pathways for the design of strong, ductile, and hydrogen tolerant materials.

Abstract: Metals are key materials for modern manufacturing and infrastructures as well as transpot and energy solutions owing to their strength and formability. These properties can severely deteriorate when they contain hydrogen, leading to unpredictable failure, an effect called hydrogen embrittlement. Here we report that hydrogen in an equiatomic CoCrFeMnNi high-entropy alloy (HEA) leads not to catastrophic weakening, but instead increases both, its strength and ductility. While HEAs originally aimed at entropy-driven phase stabilization, hydrogen blending acts opposite as it reduces phase stability. This effect, quantified by the alloy’s stacking fault energy, enables nanotwinning which increases the material’s work-hardening. These results turn a bane into a boon: hydrogen does not generally act as a harmful impurity, but can be utilized for tuning beneficial hardening mechanisms. This opens new pathways for the design of strong, ductile, and hydrogen tolerant materials.

2 citations

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10 Jun 2020

Abstract: This manuscript primarily focuses on the constraints associated with the extended version of Darcy’s law that is used to describe the multiphase flow through a porous media; and in particular, a petroleum reservoir. This manuscript clearly brings out the basics associated with the usage of Darcy’s law, and reasons out the inapplicability of the Navier-Stokes Equation in order to describe the momentum conservation in a typical petroleum reservoir. Further, this work highlights the essence of continuum-based Darcy’s macroscopic-scale equation with that of Navier-Stokes’s microscopic-scale equation. Further, the absence of capillary forces in original Darcy’s equation and extending the same by considering the concept of ‘capillary pressure’ in order to accommodate the multi-phase flow has several critical constraints associated with it. In this manuscript, all these constraints or limitations have been posed in the form of a list of basic queries that need to be addressed or at least to be understood with clarity, when applying the multi-phase fluid flow equations associated with a petroleum reservoir. This study is limited to an oil-water two-phase system.

1 citations

### Cites background from "Numerical Modeling of Coupled Fluid..."

...…flow through tight gas reservoirs, and onshore oil spill (Nitha et al., 2018; Nitha et al., 2019; Kumar and Rakesh, 2018; Kumar 2019a, 2019b; Manojkumar and Kumar, 2020; Kumar and Sekhar, 2005; Kumar et al., 2006; Sekhar and Kumar, 2006; Sekhar et al., 2006; Kumar, 2008; Kumar et al., 2008;…...

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01 Apr 2006TL;DR: The Black Oil model is applied as a guide for welling modeling of fractured porous media and nonisothermal flow as well as for solution of linear systems.

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01 Mar 2006

Abstract: Preface 1. Introduction 2. Flow and transport equations 3. Rock and fluid properties 4. Numerical methods 5. Solution of linear systems 6. Single phase flow 7. Two-phase flow 8. The Black Oil model 9. The Compositional model 10. Nonisothermal flow 11. Chemical flooding 12. Flows in fractured porous media 13. Welling modeling 14. Special topics 15. Nomenclature 16. Units Bibliography Index.

682 citations

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Abstract: In many consolidated sandstone and carbonate formations, plots of core data show that the logarithm of permeability (k) is often linearly proportional to porosity (0). The slope, intercept, and degree of scatter of these log(k)-0 trends vary from formation to formation, and these variations are attributed to differences in initial grain size and sorting, diagenetic history, and compaction history. In unconsolidated sands, better sorting systematically increases both permeability and porosity. In sands and sandstones, an increase in gravel and coarse grain size content causes k to increase even while decreasing. Diagenetic minerals in the pore space of sandstones, such as cement and some clay types, tend to decrease log(k) proportionately as 0 decreases. Models to predict permeability from porosity and other measurable rock parameters fall into three classes based on either grain, surface area, or pore dimension considerations. (Models that directly incorporate well log measurements but have no particular theoretical underpinnings form a fourth class.) Grain-based models show permeability proportional to the square of grain size times porosity raised to (roughly) the fifth power, with grain sorting as an additional parameter. Surface-area models show permeability proportional to the inverse square of pore surface area times porosity raised to (roughly) the fourth power; measures of surface area include irreducible water saturation and nuclear magnetic resonance. Pore-dimension models show permeability proportional to the square of a pore dimension times porosity raised to a power of (roughly) two and produce curves of constant pore size that transgress the linear data trends on a log(k)-0 plot. The pore dimension is obtained from mercury injection measurements and is interpreted as the pore opening size of some interconnected fraction of the pore system. The linear log(k)-0 data trends cut the curves of constant pore size from the pore-dimension models, which shows that porosity reduction is always accompanied by a reduction in characteristic pore size. The high powers of porosity of the grain-based and surface-area models are required to compensate for the inclusion of the small end of the pore size spectrum.

313 citations